# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(~(s(t_h4s_integers_int,X1)=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))=>s(t_h4s_integers_int,h4s_integers_intu_u_rem(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,X1)))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))),file('i/f/integer/INT__REM0', ch4s_integers_INTu_u_REM0)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/integer/INT__REM0', aHLu_TRUTH)).
fof(22, axiom,![X2]:(s(t_bool,X2)=s(t_bool,t)<=>p(s(t_bool,X2))),file('i/f/integer/INT__REM0', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(37, axiom,![X7]:s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X7),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))=s(t_h4s_integers_int,X7),file('i/f/integer/INT__REM0', ah4s_integers_INTu_u_ADDu_u_RID)).
fof(38, axiom,![X7]:s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,X7)))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/integer/INT__REM0', ah4s_integers_INTu_u_MULu_u_LZERO)).
fof(39, axiom,![X13]:p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,h4s_integers_abs(s(t_h4s_integers_int,X13)))))),file('i/f/integer/INT__REM0', ah4s_integers_INTu_u_ABSu_u_POS)).
fof(40, axiom,![X14]:s(t_h4s_integers_int,h4s_integers_abs(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X14)))))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X14))),file('i/f/integer/INT__REM0', ah4s_integers_INTu_u_ABSu_u_NUM)).
fof(41, axiom,![X13]:(s(t_h4s_integers_int,h4s_integers_abs(s(t_h4s_integers_int,X13)))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))<=>s(t_h4s_integers_int,X13)=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))),file('i/f/integer/INT__REM0', ah4s_integers_INTu_u_ABSu_u_EQ0)).
fof(42, axiom,![X12]:![X1]:![X13]:((p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_abs(s(t_h4s_integers_int,X12))),s(t_h4s_integers_int,h4s_integers_abs(s(t_h4s_integers_int,X1))))))&(p(s(t_bool,h4s_bools_cond(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,X13))),s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,X12))),s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X12),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))))))&?[X15]:s(t_h4s_integers_int,X13)=s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X15),s(t_h4s_integers_int,X1))),s(t_h4s_integers_int,X12)))))=>s(t_h4s_integers_int,h4s_integers_intu_u_rem(s(t_h4s_integers_int,X13),s(t_h4s_integers_int,X1)))=s(t_h4s_integers_int,X12)),file('i/f/integer/INT__REM0', ah4s_integers_INTu_u_REMu_u_UNIQUE)).
fof(43, axiom,![X7]:p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X7),s(t_h4s_integers_int,X7)))),file('i/f/integer/INT__REM0', ah4s_integers_INTu_u_LEu_u_REFL)).
fof(44, axiom,![X8]:![X7]:(p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X7),s(t_h4s_integers_int,X8))))<=>(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X7),s(t_h4s_integers_int,X8))))|s(t_h4s_integers_int,X7)=s(t_h4s_integers_int,X8))),file('i/f/integer/INT__REM0', ah4s_integers_INTu_u_LEu_u_LT)).
fof(45, axiom,![X6]:![X2]:![X16]:s(X6,h4s_bools_cond(s(t_bool,X16),s(X6,X2),s(X6,X2)))=s(X6,X2),file('i/f/integer/INT__REM0', ah4s_bools_CONDu_u_ID)).
# SZS output end CNFRefutation
